If you have a high water table forget about it. It can be done but is very expensive and difficult. What you can do build the whole thing on the top and heap soil over it.
I thought on something with old tires.

I live in an area with a high water table, and have been tossing the idea around of putting in an undergroundgreenhouse but I've been holding off for a few reasons. The high water table is definitely one. No one really has full sized basements around my area because of the water table, and those that do have a lot of moisture/mold issues. However, I don't think it's totally out of the question if you can find the right spot. Other options I've been considering are just a nicely done lean to, or converting a space inside my house into a greenhouse (my husband even said he would possibly maybe let that happen! wow!) but I haven't been able to commit to anything yet. Except for cold frames - I might commit to those. Not a big commitment